ON SOLUTIONS OF THE SHAPE EQUATION FOR MEMBRANES AND STRINGS

Classical configurations of strings and shapes of membranes in equilib rium are defined by a nonlinear equation. It is shown that this equati on has a simple form in terms of the inverse mean curvature and densit y of squared mean curvature. Broad variety of its solutions (in partic ular, kink, vortex and solitons) and corresponding possible shapes are given, Anew type of degeneracy of membrane shapes and string configur ations via the integrable Veselov-Novikov equation is discussed. (C) 1 997 Elsevier Science B.V.